In the xy-plane above, line `l` is parallel to line k. What is the value of p ?

Options

A. 4
B. 5
C. 8
D. 10

Explanation

Choice D is correct. Since lines `l` and k are parallel, the lines have the same slope. Line `l` passes through the point (-5, 0) and (0, 2), so its slope is `(0-2)/(-5-0)`, which is `(2)/(5)`. The slope of line k must also be `(2)/(5)`. Since line k has slope `(2)/(5)` and passes through the points (0, -4) and (p, 0), it follows that `(-4-0)/(0-p)=(2)/(5), or (4)/(p)=(2)/(5)`. Multiplying each side of `(4)/(p)=(2)/(5)` by 5p gives 20 = 2p, and therefore, p = 10.
Choices a, B, and C are incorrect and may result from conceptual or calculation errors.